Does the Integral of Riemman Zeta Function have a meaning?

  • #1
30
6
I have been trying to use numerical methods with this function but now I realize that I if I could suggest a Polynomial in theory, I could get some value for the Integral at least in any interval. In general, does the Integral of the Riemman dseta function has a meaning by itself?
 

Answers and Replies

  • #2
martinbn
Science Advisor
2,719
1,082
Which integral?
 
  • #3
319
108
Perhaps this one:

$$ \zeta(s)=\frac{\Gamma(1-s)}{2 \pi i} \mathop\int_{\multimap} \frac{x^{s-1}}{e^{-x}-1}dx$$

Nevertheless, one of the most beautiful constructs in Mathematics IMO.
 
  • #4
lavinia
Science Advisor
Gold Member
3,275
663
I have been trying to use numerical methods with this function but now I realize that I if I could suggest a Polynomial in theory, I could get some value for the Integral at least in any interval. In general, does the Integral of the Riemman dseta function has a meaning by itself?

I think that the Riemann zeta function is meromorphic in the entire complex plane with a single pole at 1 . It makes sense to takes its line integral along any piecewise smooth curve that goes not pass through the pole.
 

Related Threads on Does the Integral of Riemman Zeta Function have a meaning?

Replies
2
Views
2K
  • Last Post
Replies
2
Views
2K
Replies
2
Views
2K
Replies
2
Views
813
  • Last Post
Replies
14
Views
8K
  • Last Post
Replies
6
Views
3K
Top